INTRODUCTION:

The universe have an accelerated expansion at present times has caused one of the greatest problems for modern cosmology. High-precision data from the type Ia supernova, cosmic microwave background radiation and large-scale structure indicates that energy composition of universe has 4% ordinary matter, 20% dark matter and 76% dark energy [Riess et al.(1998); Perlmutter et al.(1999); Bennet et al.(2003)]. The dark energy has large negative pressure while the pressure of the dark matter is negligible. In order to interpret this expansion, many authors proposed various candidates like cosmological constant [Hinshaw et al.(2003)], dark energy models and modified gravities. But, there is still no satisfactory explanation about the origin of dark matter and dark energy.

Recently, a modification of general relativity itself was suggested to explain this accelerating universe [Vassilevich(2003)].

Amongst the nonlinear modifications of Einstein gravity, the so-called f(R) [Akbar and Cai (2006); Desouza and Faraoni (2007); Atazadeh et al. (2008); Corda (2009, 2011); Sotiriou and Faraoni (2010)] gravity, whose action is a nonlinear function of the curvature scalar R, is completely special. The f(R) theory of gravity provides the very natural gravitational alternative for dark energy. Nojiri (2007) proved that the cosmic acceleration can be directly explained by taking any negative power of the curvature . This f(R) theory helps in modification of the model to achieve the consistency with the experimental tests of solar system.

Nojiri and Odintsov (2007, 2008) derived that a unification of the early time inflation and late time acceleration is allowed in f(R) theory. Cognola et al. (2006) found it very useful in high energy physics for explaining the hierarchy problem and unification of GUTs with gravity. This f(R) theory has explained several features [Sotiriou (2006); Santose et al. (2008); Dev et al. (2008)] including solar system test [Lecian and Montani (2009)], Newtonian limit [Sotiriou (2006)], gravitational stability [Sotiriou (2007)] and singularity problem [Frolov (2008)]. These are the motivations to consider f(R) theory of gravity by large number of researchers.

The static spherically symmetric vacuum solutions of the field equations and non-vacuum solutions with perfect fluid respectively are investigated by Multamaki and Vilja (2006, 2007). Carames and Bezerra (2009) discussed spherically symmetric vacuum solutions in higher dimensions. Sharif and Kausar (2009) studied exact vacuum solutions of Bianchi type-I and type-V space times in f(R) theory of gravity. Non-vacuum solutions in Bianchi type-I and type-V using perfect fluid in f(R) gravity have been obtained by Sharif and Shamir (2010). Shamir (2011) discussed the plane symmetric vacuum Bianchi type-III cosmology in f(R) gravity. The non-vacuum solutions of Bianchi type-VIo universe with isotropic and anisotropic fluid has been analyzed by Sharif and Kausar (2011). Bianchi type-III space time with anisotropic fluid in f(R) gravity has been dealt with by Sharif and Kausar (2011). Recently, Sharif and Kausar (2011) obtained dust static spherically symmetric solutions in f(R) theory of gravity.

FRW models, being spatially homogeneous and isotropic in nature, are best fit for the representation of the large scale structure of the present universe. However, it is believed that the early universe may not have been exactly uniform. Thus, the models with anisotropic background are the most suitable to describe the early stages of the universe. Bianchi type models are among the simplest models with anisotropic background. Many authors [Reddy et al.(2009); Christodoulakis et al. (2007); Bagora (2009)]. Moussiaux et al. (1981) investigated the exact solution for vacuum Bianchi type-III model with a cosmological constant. Lorenz-Petzold (1982) studied exact Bianchi type-III solutions in the presence of electromagnetic field. Xing-Xiang (2005) discussed Bianchi type-III string cosmology with bulk viscosity in which he assumed that the expansion scalar is proportional to the shear scalar to derive the solutions. Upadhaya (2008) explored some magnetized Bianchi type-III massive string cosmological models in general relativity. Singh et al. (1991) studied some Bianchi type-III cosmological models in scalar tensor theory. Adhav et al. (2009) obtained an exact solution the vacuum Brans-Dicke field equations for the metric tensor of spatially homogeneous anisotropic Bianchi type-III model.

The main objective of this work is to find exact solutions of the field equations of the Bianchi type-III model filled with perfect fluid in the metric f(R) gravity and to discuss the recent cosmic acceleration of the universe.

6. CONCLUSION:

The Bianchi type-III model in f(R) gravity represents continuously expanding, shearing universe from the start of the big bang. For Bianchi type-III model in f(R) gravity, the dark energy has large negative pressure with indicating that the universe passes through phantom region. This conclusion supports the observational evidence of a recent supernova data [Singh et al. 2003; Alam et al. 2004; Bertolami et al. 2004].

7. REFERENCES:

1. Adhav et al. : Int.J.Theor. Phys. 47, 2002 (2008): DOI 10.1007/s10773-007-9644-3.

2. Adhav et al. : Int.J.Theor. Phys. 48, 178 (2009).

3. Akbar, M., Cai, R.G. : Phys. Lett. B 635, 7 (2006).

4. Alam et al. : Mon.Not. R. Astron. Soc. 354, 275 (2004).

5. Appelquist et al. : Modern Kaluza Klein Theories, Addison-Wesley, Reading(1987).

6. Atazadej, et al. : Phys.Lett. B 660, 275 (2008).

7. Banerjee, S., Bhui, B.: Mon. Not. R. Astron. Soc. 247, 57 (1990).

8. Bagora, A.: Astrophys. Space Sci. 319, 155 (2009).

9. Bellini, M.: Nucl.Phys. B660, 389 (2003).

10. Bennett et al. : Astrophys. J. Suppl. 148 ,1 (2003).

11. Bertolami et al.: Mon. Not. R. Astron. Soc. 353, 329 (2004).

12. Carames, TRP, Bezerra, E.R. : Eur.Phys.J. C , 64, 113 (2009).

13. Chodos, A., Detweller, S.: Phys. Rev. D 21, 2167 (1980).

14. Christodoulakis et al : Class. Quan. Grav. 24, 875 (2007).

15. Cognola, et al. : Phys.Rev. D 73, 084007 (2006).

16. Collins, et al. : Particle Physics and Cosmology.Wiley,London (1989).

17. Corda, C. : Europhys. Lett. 86, 20004 (2009).

18. Corda, C.: Astropart. Phys. 34, 587 (2011).

19. De’Souza,J.C.,Faraoni,V.: Class.Quantum Grav. 24, 3637 (2007).

20. Dev et al. : Phys. Rev. D 78, 083515 (2008).

21. Frolov,A.V.: Phys. Rev. Lett. 101, 061103 (2008).

22. Gleiser, R.J., Diaz, M.C.: Phys. Rev. D 37, 3761 (1988).

23. Hinshaw et al. : Astrophys. J. Suppl. 148, 135 (2003).

24. Ibanez, J., Verdaguer, E.: Phys. Rev. D 34, 1202 (1986).

25. Johri,V.B.,Desikan,K.: Gen.Relativ.Grav. 26, 1217 (1994).

26. KaluzaT.:Zum Unitats Prob der Physik Sitz Press.Akad.Wiss.Phys.Math.K1,966(1921).

27. Khadekar, G.S., Gaikwad, M.: Proc. Einstein Found. Int. 11, 95 (2001).

28. Klein,O.: Zeits.Phys.37,895(1926).

29. KotubUddin et al. : Class. Quantum Grav. 24 , 3951 (2007).

30. Lecian, O.M., Montani. G.: Class Quant. Grav. 26, 045014 (2009).

31. Lee, H.C.: An Introduction to Kaluza Klein Theories.World Scientific,Singapore(1984).

32. Lorenz-Petzold , D. : Astrophys. Space Sci. 85, 59 (1982).

33. Moussiaux et al : J.Phys. A . Maths. Gen. 14, 277 (1981).

34. Multamaki,T., Vilja, I. : Phys. Rev. D 74, 064022 (2006).

35. Multamaki,T., Vilja, I. : Phys. Rev. D 76, 064021(2007).

36. Nojiri S : Int. J. Geom. Meth. Mod.Phys. 4 , 115 (2007).

37. Nojiri S and Odintsov S D : J. Phys. Conf.Ser. 66, 012005 (2007).

38. Nojiri S and Odintsov S D : Phys. Rev. D 78, 046006 (2008).

39. Overdin, J.M.,Wesson,P.S.: Phys.Rep.283, 303 (1997).

40. Perlmutter et al. : Astrophys. J. 517 , 565 (1999).

41. Reddy, D.R.K., Venkateswara Rao, N.: Astrophys. Space Sci. 277, 461 (2001).

42. Reddy et al. : Int. J. Theor. Phys. 48, 2884 (2009).

43. Riess et al. : Astron. J. 116 ,1009 (1998).

44. Saha, B.: Mod. Phys. Lett. A 20, 2127 (2005).

45. Santose et al. : Phys Lett. B 669, 14 (2008).

46. Shamir, M.F. : Int. J. Theor. Phys. 50, 637 (2011).

47. Sharif, M., Kausar, H.R. : arXiv : 1102.4124v1 (2011).

48. Sharif, M., Kausar, H.R.. : AstroPhys. Space Sci. 332, 463 (2011).

49. Sharif, M., Kausar, H.R: arXiv : 1101.3372v1 (2011).

50. Sharif,M.,Shamir,M.F. : Class. Quantum Grav. 26 , 235020 (2009) .

51. Sharif,M.,Shamir,M.F. : Gen. Relativ. Grav. 42, 1557 (2010).

52. Singh, T., Agrawal,A.K. : Astrophys. Space Sci. 182, 289 (1991).

53. Singh et al. : Phys. Rev. D 68, 023522 (2003).

54. Singh et al. : Int. J. Theor. Phys. 47 , 3162 (2008).

55. Sotiriou, T.P. : Phys. Lett. B 645, 389 (2007).

56. Sotiriou,T.P., Faraoni, V. : Rev. Mod. Phys. 82, 451 (2010).

57. Sotiriou, T.P.: Class. Quant. Grav. 23, 5117 (2006).

58. Sotiriou, T.P.: Gen. Relativ. Grav. 38, 1407 (2006).

59. Upadhaya et al. : Braz. J. Phys. 38, 4 (2008).

60. Vassilevich, D.V.: Phys. Rep. 388, 279 (2003).

61. Weinberg, S.: Physics in Higher Dimensions. World Scientific, Singapore (1986).

62. Wesson, P.S.:Gen.Reltiv.Gravt.16,193(1984).

63. Wesson, P.S: Space-time Matter Theory .World Scientific, Singapore (1999).

64. Xing-Xiang , W. : Chin. Phys. Lett. 22, 29 (2005).

Received on 20.01.2013 Accepted on 05.02.2013

Research J. Science and Tech 5(1): Jan.-Mar.2013 page 85-91